But what about Ephesians 2:
4 But God, who is rich in mercy, because of His great love with which He loved us, 5 even when we were dead in trespasses, made us alive together with Christ (by grace you have been saved), 6 and raised us up together, and made us sit together in the heavenly places in Christ Jesus, 7 that in the ages to come He might show the exceeding riches of His grace in His kindness toward us in Christ Jesus. 8 For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, 9 not of works, lest anyone should boast. 10 For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them.
How can you read this scripture and say you have any part in your salvation? V.5 and V. 8 are glaring testaments to our inability to choose Christ. It appears to me, if you claim to take some action to "close the deal" on salvation, that you are claiming something you can boast about.
I certainly would agree that all the items you list (believing in Christ, repenting of my sins, confessing His name, and being baptized) are valid evidence of a new creation in Christ, but certainly not the cause.
You still have not told me how those chosen by God in the OT were saved without baptism! Has the means of salvation changed between the OT and NT?? Can people still be saved by this "old way"?
We are under a New Covenant. Those who lived under the Old Covenant, which was God's covenant with Israel, were justified by the Law. We are not under the Old Law. God's grace is what allows us to be saved, but we still must be obedient to receive that salvation(Hebrews 5:9).
Of course we can't be saved like those who lived under the Old Law. Is that a serious question? If so, then I would question what you have been taught about the relationship between the Old Testament and the New Testament. Christ gave His life as the ultimate sacrifice. This did away with the old way of atonement, which required continual sacrifices.